MAYBE

Problem:
 app(app(times(),x),app(app(plus(),y),app(s(),z))) ->
 app(app(plus(),app(app(times(),x),app(app(plus(),y),app(app(times(),app(s(),z)),0())))),
     app(app(times(),x),app(s(),z)))
 app(app(times(),x),0()) -> 0()
 app(app(times(),x),app(s(),y)) -> app(app(plus(),app(app(times(),x),y)),x)
 app(app(plus(),x),0()) -> x
 app(app(plus(),x),app(s(),y)) -> app(s(),app(app(plus(),x),y))
 app(app(map(),f),nil()) -> nil()
 app(app(map(),f),app(app(cons(),x),xs)) -> app(app(cons(),app(f,x)),app(app(map(),f),xs))
 app(app(filter(),f),nil()) -> nil()
 app(app(filter(),f),app(app(cons(),x),xs)) -> app(app(app(app(filter2(),app(f,x)),f),x),xs)
 app(app(app(app(filter2(),true()),f),x),xs) -> app(app(cons(),x),app(app(filter(),f),xs))
 app(app(app(app(filter2(),false()),f),x),xs) -> app(app(filter(),f),xs)

Proof:
 DP Processor:
  DPs:
   app#(app(times(),x),app(app(plus(),y),app(s(),z))) -> app#(app(times(),x),app(s(),z))
   app#(app(times(),x),app(app(plus(),y),app(s(),z))) -> app#(times(),app(s(),z))
   app#(app(times(),x),app(app(plus(),y),app(s(),z))) -> app#(app(times(),app(s(),z)),0())
   app#(app(times(),x),app(app(plus(),y),app(s(),z))) ->
   app#(app(plus(),y),app(app(times(),app(s(),z)),0()))
   app#(app(times(),x),app(app(plus(),y),app(s(),z))) ->
   app#(app(times(),x),app(app(plus(),y),app(app(times(),app(s(),z)),0())))
   app#(app(times(),x),app(app(plus(),y),app(s(),z))) ->
   app#(plus(),app(app(times(),x),app(app(plus(),y),app(app(times(),app(s(),z)),0()))))
   app#(app(times(),x),app(app(plus(),y),app(s(),z))) ->
   app#(app(plus(),app(app(times(),x),app(app(plus(),y),app(app(times(),app(s(),z)),0())))),
        app(app(times(),x),app(s(),z)))
   app#(app(times(),x),app(s(),y)) -> app#(app(times(),x),y)
   app#(app(times(),x),app(s(),y)) -> app#(plus(),app(app(times(),x),y))
   app#(app(times(),x),app(s(),y)) -> app#(app(plus(),app(app(times(),x),y)),x)
   app#(app(plus(),x),app(s(),y)) -> app#(app(plus(),x),y)
   app#(app(plus(),x),app(s(),y)) -> app#(s(),app(app(plus(),x),y))
   app#(app(map(),f),app(app(cons(),x),xs)) -> app#(app(map(),f),xs)
   app#(app(map(),f),app(app(cons(),x),xs)) -> app#(f,x)
   app#(app(map(),f),app(app(cons(),x),xs)) -> app#(cons(),app(f,x))
   app#(app(map(),f),app(app(cons(),x),xs)) -> app#(app(cons(),app(f,x)),app(app(map(),f),xs))
   app#(app(filter(),f),app(app(cons(),x),xs)) -> app#(f,x)
   app#(app(filter(),f),app(app(cons(),x),xs)) -> app#(filter2(),app(f,x))
   app#(app(filter(),f),app(app(cons(),x),xs)) -> app#(app(filter2(),app(f,x)),f)
   app#(app(filter(),f),app(app(cons(),x),xs)) -> app#(app(app(filter2(),app(f,x)),f),x)
   app#(app(filter(),f),app(app(cons(),x),xs)) -> app#(app(app(app(filter2(),app(f,x)),f),x),xs)
   app#(app(app(app(filter2(),true()),f),x),xs) -> app#(filter(),f)
   app#(app(app(app(filter2(),true()),f),x),xs) -> app#(app(filter(),f),xs)
   app#(app(app(app(filter2(),true()),f),x),xs) -> app#(cons(),x)
   app#(app(app(app(filter2(),true()),f),x),xs) -> app#(app(cons(),x),app(app(filter(),f),xs))
   app#(app(app(app(filter2(),false()),f),x),xs) -> app#(filter(),f)
   app#(app(app(app(filter2(),false()),f),x),xs) -> app#(app(filter(),f),xs)
  TRS:
   app(app(times(),x),app(app(plus(),y),app(s(),z))) ->
   app(app(plus(),app(app(times(),x),app(app(plus(),y),app(app(times(),app(s(),z)),0())))),
       app(app(times(),x),app(s(),z)))
   app(app(times(),x),0()) -> 0()
   app(app(times(),x),app(s(),y)) -> app(app(plus(),app(app(times(),x),y)),x)
   app(app(plus(),x),0()) -> x
   app(app(plus(),x),app(s(),y)) -> app(s(),app(app(plus(),x),y))
   app(app(map(),f),nil()) -> nil()
   app(app(map(),f),app(app(cons(),x),xs)) -> app(app(cons(),app(f,x)),app(app(map(),f),xs))
   app(app(filter(),f),nil()) -> nil()
   app(app(filter(),f),app(app(cons(),x),xs)) -> app(app(app(app(filter2(),app(f,x)),f),x),xs)
   app(app(app(app(filter2(),true()),f),x),xs) -> app(app(cons(),x),app(app(filter(),f),xs))
   app(app(app(app(filter2(),false()),f),x),xs) -> app(app(filter(),f),xs)
  Open